How would you explain the V-I curve for High Tc supercondctors? I am reading a section on this topic although we haven ;t studied it and am confused as to how one can explain the curve?

It starts off linear then has a flat region and then is linear again.
What would be the explanation of such a curve? Why does it look the way it does?

James

You left out a very important part of your question, that the V-I (or more accurately, the I-V curve) such as the one you described came from a tunneling measurement!

The linear part shouldn't be surprising - this is exactly Ohm's Law. (Note that even this isn't true for all superconductors, especially high-Tc superconductors. There are many tunneling data extended to high voltages that do not show such linearity). The "flat" part that is near zero bias is due to the fact that there is an energy gap in a superconductor's density of states (DOS). The energy gap corresponds to the pairing energy that forms the cooper pairs. So when the bias voltage is smaller than this pairing energy, you cannot break apart the cooper pair to form individual electrons.

If you are looking at IV curve for a superconductor-insulator-normal metal tunneling, then at a bias less than this pairing energy, you will not get individual electrons to tunnel across the insulator. If it's a superconductor-insulator-superconductor junction, then the flat curve will start at twice the paring energy. You need to study and understand the superconducting DOS and tunneling spectroscopy to know why such things occur.

The last part is the Josephson junction right? Superconductor-insulator-superconductor?

Usually, it isn't called the josephson junction, because not all SIS junction produces josephson current. There are criteria that have to be met for it to exhibit such phenomena.

Now, what about the V-flux graph which is periodic in nature? Is there a similar explanation of this?

V-flux graph? What's that?

Does this mean that the resistivity is zero? That is, the electron pairs experience no resistance?

Resistivity (at least DC resistivity) is ALWAYS zero in the superconductor. What you are asking for is the TUNNEL JUNCTION RESISTIVITY. The IV curve is for the current tunneling through the insulator, not the current IN the superconductor. When the IV curve is flat in the gap region, the resistivity is INFINITE. This is because you have almost zero current tunneling through the insulator.

V-flux is the voltage versus applied magnetic flux. It is like a sine function..periodic.

You really should learn to give out as complete of an information as possible, especially when you are asking for FAVORS in getting answers to your questions. If I hadn't worked in the field of superconductivity and done tunneling work, none of what you are asking would have made any sense. In this case, can you figure out why just by saying "V-flux is the voltage versus applied magnetic flux" is rather ambiguous? I mean, what "voltage" applied where? What is the geometry of the magnetic field? It's orientation? Are we dealing with only high-Tc superconductors (which are Type II superconductors) or just superconductors in general? Do I get to know exactly what it is you're reading so that I can double check if what you are seeing and interpreting is correct?

I just saw the result of an experiment which gave voltage versus applied flux graph of a High Tc superconductor. The experiment just investigated the basic properties such as what you helped me with..the I-V curve. It also investigated the FLUX-V curve. The experiment involved using a Josephson junction and a SQUID chip.

This explanation describing the FLUX-V seems a bit confusing to me:

Applying an external magnetic field to a dc SQUID causes the voltage across the SQUID to change periodically as the field is varied. The periodicity of the voltage
modulation is governed by a fundamental quantity known as the magnetic flux quantum
or "fluxon." Briefly, the voltage undergoes a complete cycle of modulation each time a
quantum of flux passes through the superconducting loop that comprises the SQUID.
Since magnetic flux is the product of magnetic field times area, the magnetic field period of these voltage oscillations is determined by the geometry of the SQUID.

This explanation does not incorporate the critical temperature (and/or critical current) that I was hoping to relate the graph to. I just wanted to know how the critical temperature can be used to explain the periodic function.

I just saw the result of an experiment which gave voltage versus applied flux graph of a High Tc superconductor. The experiment just investigated the basic properties such as what you helped me with..the I-V curve. It also investigated the FLUX-V curve. The experiment involved using a Josephson junction and a SQUID chip.

And you are unable to give an exact citation of this "thing" that you are reading? I have access to almost every physics journal in publication. I could have easily looked this up, rather than having to rely on 2nd party interpretation.

This explanation describing the FLUX-V seems a bit confusing to me:

Applying an external magnetic field to a dc SQUID causes the voltage across the SQUID to change periodically as the field is varied. The periodicity of the voltage
modulation is governed by a fundamental quantity known as the magnetic flux quantum
or "fluxon." Briefly, the voltage undergoes a complete cycle of modulation each time a
quantum of flux passes through the superconducting loop that comprises the SQUID.
Since magnetic flux is the product of magnetic field times area, the magnetic field period of these voltage oscillations is determined by the geometry of the SQUID.

But that's what a SQUID is supposed to do, detect a magnetic field. The "modulation" in current (or voltage) is analogous to the fraunhoffer pattern one gets from interference experiment. Supercurrents going through one arm of the SQUID experience a phase shift due to the field when compared to the supercurrent flowing in the other arm of the SQUID.

This explanation does not incorporate the critical temperature (and/or critical current) that I was hoping to relate the graph to. I just wanted to know how the critical temperature can be used to explain the periodic function.

James

I have no idea what this is or why the modulations would have anything to do with Tc.

I have one last question..how could one explain the resistance temperature curve of a SQUID. This is zero until the transition temperature around 90 K and then shoots up vertically and then has a linear dependence. How could this behaviour be explained?

This sounds an awful lot like you're just asking why a type I SC exhibits zero dc resitivity below Tc. Or it may just be my igorance of all things squid. (If I'm not mistaken, they do make type I squids...don't they ?)

If the above is, in fact your question, I highly recommend you find some intro to superconductivity and read that before you jump into the guts of a squid. Kittel or Ashcroft may be a good place to start, and if you want more, there's Tinkham. You might even try looking for review articles from Physicsweb or other such places.

Just physically understanding what is happening in the various regions. The resistance is zero until around 90 K for the YBCO SQUID. How can the rest of the graph be explained? Its structure? or shape that is.

The behavior of the cuprates (YBCO included) above Tc is still not well understood. All the transport properties (including the dc resistivity) exhibit non-fermi liquid behavior. In other words they do not behave like most normal metals (or insulators in this case) where electron-electron interactions play a negligible role in the transport properties.

But ignoring these difficulties, it should not be hard to see why the resistivity increases with temperature. At high temperatures, the dominant cause of the resistivity is phonon scattering. The phonon density being proportional to the temperature, one would expect the resistivity to also increase with the temperature. As you lower the temperature, however, impurity/defect scattering becomes noticeable and so, the zero temperature limit would be a purely imperfection related (non-zero) term. However, at Tc, the material goes through a second (perhaps first even ?) order transition, where the resistivity falls to zero with pair formation. In the case of optimally doped YBCO (which I think is what gets used in SQUIDs), we are spared the additional weirdness arising from the "pseudogap".

Notice that the explanation, to this level of hand-waviness is no different from that for a Type I SC.

If you want a better explanation here, you'll have to get it out of ZapperZ or nbo10. Better still, you might do a search here on superconductivity and see what you come up with.